What is the function of g

Question

Let f(x)=|x|. Write a function g whose graph is a vertical shrink by a factor of 1/2 followed by a translation 2 units up of the graph of f.

Answer 1

To vertically stretch or shrink multiply the entire function by whatever value you are wanting to stretch or shrink with:

g(x) = 1⁄2 (f(x))

g(x) = 1⁄2 (lxl)

To vertically shift the graph, add to the entire function what value you would like to shift up by or subtract by whatever value you would like to shift down by:

g(x) = f(x) + 2

g(x) = lxl + 2

So together that would look like:

g(x) = 1⁄2( lxl) + 2

Answer 2

Vertical shrink by 1/2

g(x) = (1/2)|x|

Translation 2 units up.

g(x) = (1/2)|x| + 2

It doesn't ask, but a translation left or right would be inside the absolute value sign and opposite the given direction.

Translation 5 units left.

g(x) = (1/2)|x + 5| + 2